# Let R be the set of real numbers, f : R?R be the function defined by f (x) = 4x + 3, x ? R. Show that f is invertible. Find the inverse of f ?

Jitender Singh IIT Delhi
8 years ago
Ans:
$f : R\rightarrow R$
$f(x) = 4x + 3$
Since range of function is equal to co-domain, so it is onto function.
It is straight line, so it is clear from the graph that it is one to one function.
-> f(x) is bijective function, so it can be invertible.
$x\rightarrow f^{-1}(x)$
$f(f^{-1}(x)) = 4f^{-1}(x) + 3$
$f(f^{-1}(x)) = x$
$f^{-1}(x) = \frac{x-3}{4}$
Thanks & Regards
Jitender Singh
IIT Delhi